nalgebra/geometry/
similarity_conversion.rs

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1use num::Zero;
2
3use simba::scalar::{RealField, SubsetOf, SupersetOf};
4use simba::simd::{PrimitiveSimdValue, SimdRealField, SimdValue};
5
6use crate::base::allocator::Allocator;
7use crate::base::dimension::{DimMin, DimNameAdd, DimNameSum, U1};
8use crate::base::{Const, DefaultAllocator, OMatrix, Scalar};
9
10use crate::geometry::{
11    AbstractRotation, Isometry, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
12};
13
14/*
15 * This file provides the following conversions:
16 * =============================================
17 *
18 * Similarity -> Similarity
19 * Similarity -> Transform
20 * Similarity -> Matrix (homogeneous)
21 */
22
23impl<T1, T2, R1, R2, const D: usize> SubsetOf<Similarity<T2, R2, D>> for Similarity<T1, R1, D>
24where
25    T1: RealField + SubsetOf<T2>,
26    T2: RealField + SupersetOf<T1>,
27    R1: AbstractRotation<T1, D> + SubsetOf<R2>,
28    R2: AbstractRotation<T2, D>,
29{
30    #[inline]
31    fn to_superset(&self) -> Similarity<T2, R2, D> {
32        Similarity::from_isometry(self.isometry.to_superset(), self.scaling().to_superset())
33    }
34
35    #[inline]
36    fn is_in_subset(sim: &Similarity<T2, R2, D>) -> bool {
37        crate::is_convertible::<_, Isometry<T1, R1, D>>(&sim.isometry)
38            && crate::is_convertible::<_, T1>(&sim.scaling())
39    }
40
41    #[inline]
42    fn from_superset_unchecked(sim: &Similarity<T2, R2, D>) -> Self {
43        Similarity::from_isometry(
44            sim.isometry.to_subset_unchecked(),
45            sim.scaling().to_subset_unchecked(),
46        )
47    }
48}
49
50impl<T1, T2, R, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Similarity<T1, R, D>
51where
52    T1: RealField,
53    T2: RealField + SupersetOf<T1>,
54    C: SuperTCategoryOf<TAffine>,
55    R: AbstractRotation<T1, D>
56        + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>
57        + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
58    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, // needed by .determinant()
59    DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
60        + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
61        + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
62    // + Allocator<(usize, usize), D>
63    // + Allocator<T1, D>
64    // + Allocator<T1, D, D>
65    // + Allocator<T2, D, D>
66    // + Allocator<T2, D>,
67{
68    #[inline]
69    fn to_superset(&self) -> Transform<T2, C, D> {
70        Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
71    }
72
73    #[inline]
74    fn is_in_subset(t: &Transform<T2, C, D>) -> bool {
75        <Self as SubsetOf<_>>::is_in_subset(t.matrix())
76    }
77
78    #[inline]
79    fn from_superset_unchecked(t: &Transform<T2, C, D>) -> Self {
80        Self::from_superset_unchecked(t.matrix())
81    }
82}
83
84impl<T1, T2, R, const D: usize>
85    SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>
86    for Similarity<T1, R, D>
87where
88    T1: RealField,
89    T2: RealField + SupersetOf<T1>,
90    R: AbstractRotation<T1, D>
91        + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>
92        + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
93    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, // needed by .determinant()
94    DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
95        + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
96        + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, // + Allocator<(usize, usize), D>
97                                                                             // + Allocator<T1, D>
98                                                                             // + Allocator<T1, D, D>
99                                                                             // + Allocator<T2, D, D>
100                                                                             // + Allocator<T2, D>
101{
102    #[inline]
103    fn to_superset(&self) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> {
104        self.to_homogeneous().to_superset()
105    }
106
107    #[inline]
108    fn is_in_subset(m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>) -> bool {
109        let mut rot = m.fixed_slice::<D, D>(0, 0).clone_owned();
110        if rot
111            .fixed_columns_mut::<1>(0)
112            .try_normalize_mut(T2::zero())
113            .is_some()
114            && rot
115                .fixed_columns_mut::<1>(1)
116                .try_normalize_mut(T2::zero())
117                .is_some()
118            && rot
119                .fixed_columns_mut::<1>(2)
120                .try_normalize_mut(T2::zero())
121                .is_some()
122        {
123            // TODO: could we avoid explicit the computation of the determinant?
124            // (its sign is needed to see if the scaling factor is negative).
125            if rot.determinant() < T2::zero() {
126                rot.fixed_columns_mut::<1>(0).neg_mut();
127                rot.fixed_columns_mut::<1>(1).neg_mut();
128                rot.fixed_columns_mut::<1>(2).neg_mut();
129            }
130
131            let bottom = m.fixed_slice::<1, D>(D, 0);
132            // Scalar types agree.
133            m.iter().all(|e| SupersetOf::<T1>::is_in_subset(e)) &&
134            // The normalized block part is a rotation.
135            // rot.is_special_orthogonal(T2::default_epsilon().sqrt()) &&
136            // The bottom row is (0, 0, ..., 1)
137            bottom.iter().all(|e| e.is_zero()) && m[(D, D)] == T2::one()
138        } else {
139            false
140        }
141    }
142
143    #[inline]
144    fn from_superset_unchecked(
145        m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
146    ) -> Self {
147        let mut mm = m.clone_owned();
148        let na = mm.fixed_slice_mut::<D, 1>(0, 0).normalize_mut();
149        let nb = mm.fixed_slice_mut::<D, 1>(0, 1).normalize_mut();
150        let nc = mm.fixed_slice_mut::<D, 1>(0, 2).normalize_mut();
151
152        let mut scale = (na + nb + nc) / crate::convert(3.0); // We take the mean, for robustness.
153
154        // TODO: could we avoid the explicit computation of the determinant?
155        // (its sign is needed to see if the scaling factor is negative).
156        if mm.fixed_slice::<D, D>(0, 0).determinant() < T2::zero() {
157            mm.fixed_slice_mut::<D, 1>(0, 0).neg_mut();
158            mm.fixed_slice_mut::<D, 1>(0, 1).neg_mut();
159            mm.fixed_slice_mut::<D, 1>(0, 2).neg_mut();
160            scale = -scale;
161        }
162
163        let t = m.fixed_slice::<D, 1>(0, D).into_owned();
164        let t = Translation {
165            vector: crate::convert_unchecked(t),
166        };
167
168        Self::from_parts(
169            t,
170            crate::convert_unchecked(mm),
171            crate::convert_unchecked(scale),
172        )
173    }
174}
175
176impl<T: SimdRealField, R, const D: usize> From<Similarity<T, R, D>>
177    for OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
178where
179    Const<D>: DimNameAdd<U1>,
180    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
181    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, // + Allocator<T, D>
182{
183    #[inline]
184    fn from(sim: Similarity<T, R, D>) -> Self {
185        sim.to_homogeneous()
186    }
187}
188
189impl<T: Scalar + Zero + PrimitiveSimdValue, R, const D: usize>
190    From<[Similarity<T::Element, R::Element, D>; 2]> for Similarity<T, R, D>
191where
192    T: From<[<T as SimdValue>::Element; 2]>,
193    R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 2]>,
194    R::Element: AbstractRotation<T::Element, D>,
195    T::Element: Scalar + Zero + Copy,
196    R::Element: Scalar + Zero + Copy,
197{
198    #[inline]
199    fn from(arr: [Similarity<T::Element, R::Element, D>; 2]) -> Self {
200        let iso = Isometry::from([arr[0].isometry, arr[1].isometry]);
201        let scale = T::from([arr[0].scaling(), arr[1].scaling()]);
202
203        Self::from_isometry(iso, scale)
204    }
205}
206
207impl<T: Scalar + Zero + PrimitiveSimdValue, R, const D: usize>
208    From<[Similarity<T::Element, R::Element, D>; 4]> for Similarity<T, R, D>
209where
210    T: From<[<T as SimdValue>::Element; 4]>,
211    R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 4]>,
212    R::Element: AbstractRotation<T::Element, D>,
213    T::Element: Scalar + Zero + Copy,
214    R::Element: Scalar + Zero + Copy,
215{
216    #[inline]
217    fn from(arr: [Similarity<T::Element, R::Element, D>; 4]) -> Self {
218        let iso = Isometry::from([
219            arr[0].isometry,
220            arr[1].isometry,
221            arr[2].isometry,
222            arr[3].isometry,
223        ]);
224        let scale = T::from([
225            arr[0].scaling(),
226            arr[1].scaling(),
227            arr[2].scaling(),
228            arr[3].scaling(),
229        ]);
230
231        Self::from_isometry(iso, scale)
232    }
233}
234
235impl<T: Scalar + Zero + PrimitiveSimdValue, R, const D: usize>
236    From<[Similarity<T::Element, R::Element, D>; 8]> for Similarity<T, R, D>
237where
238    T: From<[<T as SimdValue>::Element; 8]>,
239    R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 8]>,
240    R::Element: AbstractRotation<T::Element, D>,
241    T::Element: Scalar + Zero + Copy,
242    R::Element: Scalar + Zero + Copy,
243{
244    #[inline]
245    fn from(arr: [Similarity<T::Element, R::Element, D>; 8]) -> Self {
246        let iso = Isometry::from([
247            arr[0].isometry,
248            arr[1].isometry,
249            arr[2].isometry,
250            arr[3].isometry,
251            arr[4].isometry,
252            arr[5].isometry,
253            arr[6].isometry,
254            arr[7].isometry,
255        ]);
256        let scale = T::from([
257            arr[0].scaling(),
258            arr[1].scaling(),
259            arr[2].scaling(),
260            arr[3].scaling(),
261            arr[4].scaling(),
262            arr[5].scaling(),
263            arr[6].scaling(),
264            arr[7].scaling(),
265        ]);
266
267        Self::from_isometry(iso, scale)
268    }
269}
270
271impl<T: Scalar + Zero + PrimitiveSimdValue, R, const D: usize>
272    From<[Similarity<T::Element, R::Element, D>; 16]> for Similarity<T, R, D>
273where
274    T: From<[<T as SimdValue>::Element; 16]>,
275    R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 16]>,
276    R::Element: AbstractRotation<T::Element, D>,
277    T::Element: Scalar + Zero + Copy,
278    R::Element: Scalar + Zero + Copy,
279{
280    #[inline]
281    fn from(arr: [Similarity<T::Element, R::Element, D>; 16]) -> Self {
282        let iso = Isometry::from([
283            arr[0].isometry,
284            arr[1].isometry,
285            arr[2].isometry,
286            arr[3].isometry,
287            arr[4].isometry,
288            arr[5].isometry,
289            arr[6].isometry,
290            arr[7].isometry,
291            arr[8].isometry,
292            arr[9].isometry,
293            arr[10].isometry,
294            arr[11].isometry,
295            arr[12].isometry,
296            arr[13].isometry,
297            arr[14].isometry,
298            arr[15].isometry,
299        ]);
300        let scale = T::from([
301            arr[0].scaling(),
302            arr[1].scaling(),
303            arr[2].scaling(),
304            arr[3].scaling(),
305            arr[4].scaling(),
306            arr[5].scaling(),
307            arr[6].scaling(),
308            arr[7].scaling(),
309            arr[8].scaling(),
310            arr[9].scaling(),
311            arr[10].scaling(),
312            arr[11].scaling(),
313            arr[12].scaling(),
314            arr[13].scaling(),
315            arr[14].scaling(),
316            arr[15].scaling(),
317        ]);
318
319        Self::from_isometry(iso, scale)
320    }
321}
nalgebra/geometry/similarity_conversion.rs

nalgebra/geometry/
similarity_conversion.rs
